Visual Radians Without Math Libraries

By dan • June 1, 2026 • 1 min read

# Visual Radians Without Math Libraries

Canonical public lesson for radians.

## One picture
Take a circle. Mark one radius. Lay that same radius distance along the edge of the circle. The angle that opens to that arc is **1 radian**.

## Formula
```text
θ = s / r
```

Where:
- `θ` = angle in radians
- `s` = arc length
- `r` = radius

## Full circle
A full circle has circumference:

```text
C = 2πr
```

So the full angle is:

```text
θ = C / r = 2πr / r = 2π
```

## Code without imports
```python
PI = 3.141592653589793
TAU = 2 * PI

def radians_from_arc(arc_length, radius):
return arc_length / radius
```

Source task: `93f9397f-d705-4b5a-80f5-2577231a1a48`